尤 琼, 史治宇. 基于区间B样条小波有限元的移动荷载识别[J]. 工程力学, 2011, 28(5): 35-040.
引用本文: 尤 琼, 史治宇. 基于区间B样条小波有限元的移动荷载识别[J]. 工程力学, 2011, 28(5): 35-040.
YOU Qiong, SHI Zhi-yu. MOVING FORCE IDENTIFICATION BASED ON B-SPLINE WAVELET ON THE INTERVAL[J]. Engineering Mechanics, 2011, 28(5): 35-040.
Citation: YOU Qiong, SHI Zhi-yu. MOVING FORCE IDENTIFICATION BASED ON B-SPLINE WAVELET ON THE INTERVAL[J]. Engineering Mechanics, 2011, 28(5): 35-040.

基于区间B样条小波有限元的移动荷载识别

MOVING FORCE IDENTIFICATION BASED ON B-SPLINE WAVELET ON THE INTERVAL

  • 摘要: 小波有限元以区间B样条小波尺度函数为插值函数构造小波有限元单元,并通过单元转换矩阵建立小波空间与物理空间各参数之间的关系。采用动态规划法与Tikhonov正则化法识别移动荷载,避免了直接处理反问题时的振荡与数值计算病态解等问题。算例采用所测得的部分离散点的动态响应数据为已知信息,验证了小波有限元的优越性及小波的多尺度特性,仿真结果表明,在相同条件下与传统有限元模型相比,小波有限元模型单元较少,识别精度较高;且可根据不同的识别精度要求自由选取所需的小波尺度。

     

    Abstract: The elements in the WFEM (wavelet finite element method) are constructed by the scale function of BSWI (B-spline wavelet on the interval), and an elemental transformation matrix is formed to combine the parameters in both wavelet and physical spaces. The dynamic programming technique and Tikhonov regularization are used for the moving force identification, which inherently avoids large fluctuations and ill-condition. The superiority of WFEM and multi-scale property of BSWI is validated in the numerical cases using several distributed measured dynamic responses. The result shows WFEM gives more accurate results over the TFEM (traditional finite element method) under the same condition with fewer elements; and the scales can be conveniently changed and chosen to satisfy any identification precision we desired.

     

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